Jahn-Teller Effect in theT2g4Excited State ofV2+in MgO

Abstract

The lowest frequency ("no-phonon") line of the ${}_{}{}^4{}_{}{}^{}A_2^{}{}_{}{}^{}\to {}_{}{}^4{}_{}{}^{}T_2^{}{}_{}{}^{}$ transition of ${\mathrm{V}}^{2+}$ in MgO is a doublet which can be split, shifted, and polarized by uniaxial stress. Both the zero-stress spectrum and the effect of stress are inconsistent with cubic symmetry in the ${}_{}{}^4{}_{}{}^{}T_2^{}{}_{}{}^{}$ state, or with a simple static Jahn-Teller effect. The major consequence of the Jahn-Teller effect is distortion along [100]-type axes, but in addition ${\tau }_{2g}$ vibrations play an important role. The data can be fitted with an effective Hamiltonian which contains terms of $T_{2g}$ symmetry. These terms mix the three vibronic states corresponding to the three possible directions of static distortion. The resulting vibronic energy levels form a singlet and a doublet, the latter lying lower. We can calculate the effect of stress quantitatively, using the one-electron matrix elements of strain found by experiments on the ${}_{}{}^2{}_{}{}^{}E$ state (which shows no Jahn-Teller effect), and obtain excellent agreement with experiment. A tentative explanation of the effective Hamiltonian in terms of more fundamental concepts is suggested.